Similar to works [1]}, [2]}, choosing \(\gamma =\frac{1}{1+\lambda _f}\)  and \(\beta =\frac{1}{2\gamma }\) , we have
\(\mathbf {F}^{k}-\gamma \nabla h_s(\mathbf {F}^{k})&=&\Big ((1-\gamma )\mathbf {I}-\gamma \lambda _f\tilde{\mathbf {L}}\Big )\mathbf {F}^{k}+\gamma \mathbf {X}_{trans}, \nonumber \\&=&\gamma \mathbf {X}_{trans} + (1-\gamma )\tilde{\mathbf {A}}\mathbf {F}^{k},\) 
